why dont use Vector Cross Product as Multiplikation ?

[cKleinhuis]

i just read about algebras, and found that vektor cross product can be used to define the multiplication, perhaps it
could lead to nice results, although definitive no mandelbrot shapes, but worth a try

[hobold]

The vector cross product of a vector X with itself is always the zero vector. In other words, the cross product cannot directly be used for the squaring of z^2 + c. There could well be other uses for the cross product in other formulas, though.

[M Benesi]

  I've used dot product to find angles between a vector and an axis.  The same can be done with the cross product.  Determining what to do with those angles is the issue .....

[cKleinhuis]

The vector cross product of a vector X with itself is always the zero vector. In other words, the cross product cannot directly be used for the squaring of z^2 + c. There could well be other uses for the cross product in other formulas, though.

i see, that makes no sense

[fractower]

Cross products can be very useful for producing rotations. Specifically if you have two vectors and then the cross product will be a vector which is perpendicular and . The magnitude of   will be proportional to . Where is the angle between and . The part is mostly a pain since you really want to normalize . Give a normalize vector one can easily produce a rotation matrix (Google has a good description). I keep a set of tinker toys handy for when I need to do vector operations.

I have attached a pointer to an image and a write up of an algorithm I have been playing with that makes a lot of use of cross products..

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3286
http://www.fractalforums.com/new-theories-and-research/tinker-towers/msg21004/#msg21004

I have tried throwing random vector operations together. For the most part the results are boring, If I come up with something interesting however, I am perfectly willing to say "I meant to do that."